Results for 'Implication (Logic'

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  1.  25
    On the Role of Implication in Formal Logic.Jonathan P. Seldin - 2000 - Journal of Symbolic Logic 65 (3):1076-1114.
    Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a "classical" version of the system. (...)
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  2.  9
    Propositional Logic Extended with a Pedagogically Useful Relevant Implication.Diderik Batens - 2013 - Logic and Logical Philosophy.
    First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a relevant logic that (...)
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  3.  32
    A Dynamic Characterization of the Pure Logic of Relevant Implication.Diderik Batens - 2001 - Journal of Philosophical Logic 30 (3):267-280.
    This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual settheoretical interpretation. (ii) A proof format may display (...)
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  4.  4
    On a Four-Valued Modal Logic with Deductive Implication.Marcelo E. Coniglio & Martín Figallo - 2014 - Bulletin of the Section of Logic 43 (1/2):1-18.
    In this paper we propose to enrich the four-valued modal logic associated to Monteiro's Tetravalent modal algebras (TMAs) with a deductive implication, that is, such that the Deduction Meta-theorem holds in the resulting logic. All this lead us to establish some new connections between TMAs, symmetric (or involutive) Boolean algebras, and modal algebras for extensions of S5, as well as their logical counterparts.
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  5.  11
    Admissible Rules in the Implication–Negation Fragment of Intuitionistic Logic.Petr Cintula & George Metcalfe - 2010 - Annals of Pure and Applied Logic 162 (2):162-171.
    Uniform infinite bases are defined for the single-conclusion and multiple-conclusion admissible rules of the implication–negation fragments of intuitionistic logic and its consistent axiomatic extensions . A Kripke semantics characterization is given for the structurally complete implication–negation fragments of intermediate logics, and it is shown that the admissible rules of this fragment of form a PSPACE-complete set and have no finite basis.
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  6.  47
    Relevant Implication and the Case for a Weaker Logic.Ross T. Brady - 1996 - Journal of Philosophical Logic 25 (2):151 - 183.
    We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with (...)
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  7.  4
    Contenability and the Logic of Consequential Implication.Claudio Pizzi - 2004 - Logic Journal of the IGPL 12 (6):561-579.
    The aim of the paper is to outline a treatment of cotenability inspired by a perspective which had strong roots in ancient logic since Chrysippus and was partially recovered in the XX Century by E. Nelson and the exponents of so-called connexive logic. Consequential implication is a modal reinterpretation of connexive implication which permits a simple reconstruction of Aristotle's square of conditionals, in which proper place is given not only to ordinary cotenability between A and B, represented by (...)
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  8. Relevant Implication and the Case for a Weaker Logic: Dedicated to Robert K. Meyer on the Occasion of His 60th Birthday.Ross T. Brady - 1996 - Journal of Philosophical Logic 25 (2):151-183.
    We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with (...)
     
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  9.  15
    A Weak Intuitionistic Propositional Logic with Purely Constructive Implication.Mitsuhiro Okada - 1987 - Studia Logica 46 (4):371 - 382.
    We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.
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  10.  15
    Proof and Implication in Mill's Philosophy of Logic.Geoffrey Scarre - 1984 - History and Philosophy of Logic 5 (1):19-37.
    Following a brief preface, the second section of this paper discusses Mill's early reflections on the problem of how deductive inference can be illuminating. In the third section it is suggested that in his Logic Mill misconstrued the feature that the premises of a logically valid argument contain the conclusion as the ground of a charge that deductive proof is question-begging. The fourth section discusses the nature of the traditional petitio objection to syllogism, and the fifth shows that Mill had (...)
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  11.  17
    On Two Fragments with Negation and Without Implication of the Logic of Residuated Lattices.Félix Bou, Àngel García-Cerdaña & Ventura Verdú - 2006 - Archive for Mathematical Logic 45 (5):615-647.
    The logic of (commutative integral bounded) residuated lattices is known under different names in the literature: monoidal logic [26], intuitionistic logic without contraction [1], H BCK [36] (nowadays called by Ono), etc. In this paper we study the -fragment and the -fragment of the logical systems associated with residuated lattices, both from the perspective of Gentzen systems and from that of deductive systems. We stress that our notion of fragment considers the full consequence relation admitting hypotheses. It results that this (...)
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  12. Logic and/in Psychology: The Paradoxes of Material Implication and Psychologism in the Cognitive Science of Human Reasoning.Walter Schroyens - 2010 - In Mike Oaksford & Nick Chater (eds.), Cognition and Conditionals: Probability and Logic in Human Thinking. Oxford University Press.
     
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  13.  14
    The Logic of Implication.Noel Balzer - 1990 - Journal of Value Inquiry 24 (4):253-268.
    The principles that AN INSTANCE OF A CLASS IS THE CLASS and A CLASS IS AN INSTANCE OF ITSELF allow for the so called LAWS OF THOUGHTIDENTITY - WHAT IS, IS.CONTRADICTION - NOTHING BOTH IS and IS NOT.EXCLUDED MIDDLE - EVERYTHING IS or IS NOT.and allow us to adopt a bivalent system. Everything essential for primary logic is provided.Though this is not the place to discuss it, it should be noted that the development of general logic with its current theories (...)
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  14.  2
    LKQ and LKT: Sequent Calculi for Second Order Logic Based Upon Dual Linear Decompositions of Classical Implication.Vincent Danos, Jean-Baptiste Joinet & Harold Schellinx - 1995 - In Jean-Yves Girard, Yves Lafont & Laurent Regnier (eds.), Advances in Linear Logic. Cambridge University Press. pp. 222--211.
  15.  9
    On the Logic of Contingent Relevant Implication: A Conceptual Incoherence in the Intuitive Interpretation of ${\Rm R}$.Mark Lance - 1988 - Notre Dame Journal of Formal Logic 29 (4):520-529.
  16.  14
    Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication.Francine F. Abeles - 2014 - History and Philosophy of Logic 35 (1):1-14.
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  17.  3
    Quantum Logic with Implication.J. Jay Zeman - 1979 - Notre Dame Journal of Formal Logic 20 (4):723-728.
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  18.  2
    Anderson's Deontic Logic and Relevant Implication.Robert P. McArthur - 1981 - Notre Dame Journal of Formal Logic 22 (2):145-154.
  19.  7
    A Simplified Account of Validity and Implication for Quantificational Logic.Hugues LeBlanc - 1968 - Journal of Symbolic Logic 33 (2):231-235.
  20.  9
    On an Implication Function in Many-Valued Systems of Logic.Z. P. Dienes - 1949 - Journal of Symbolic Logic 14 (2):95-97.
  21.  3
    Review: E. J. Ashworth, Propositional Logic in the Sixteenth and Early Seventeenth Centuries; E. J. Ashworth, Petrus Fonseca and Material Implication[REVIEW]Martin M. Tweedale - 1971 - Journal of Symbolic Logic 36 (2):323-324.
  22.  3
    Shukla Anjan. A Set of Axioms for the Propositional Calculus with Implication and Converse Non-Implication. Notre Dame Journal of Formal Logic, Vol. 6 No. 2 (1965), Pp. 123–128. [REVIEW]John Bacon - 1997 - Journal of Symbolic Logic 31 (4):664-664.
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  23.  1
    Anderson Alan Ross and Belnap Nuel D. Jr., Modalities in Ackermann's “Rigorous Implication.” The Journal of Symbolic Logic, Vol. 24 No. 2 , Pp. 107–111. [REVIEW]A. Bayart - 1969 - Journal of Symbolic Logic 34 (1):120.
  24.  1
    Martin Robert L.. Toward a Solution to the Liar Paradox. The Philosophical Review, Vol. 76, Pp. 279–311.Martin Robert L.. On Grelling's Paradox. The Philosophical Review, Vol. 77 , Pp. 321–331.Van Fraassen Bas C.. Presupposition, Implication, and Self-Reference. The Journal of Philosophy, Vol. 65 , Pp. 136–152.Skyrms Brian. Return of the Liar: Three-Valued Logic and the Concept of Truth. American Philosophical Quarterly, Vol. 7 , Pp. 153–161.Martin Robert L.. Preface. The Paradox of the Liar, Edited by Martin Robert L., Yale University Press, New Haven and London 1970, P. Vii. [REVIEW]James Cargile - 1975 - Journal of Symbolic Logic 40 (4):584-587.
  25.  1
    Dienes Z. P.. On an Implication Function in Many-Valued Systems of Logic.Alonzo Church & Nicholas Rescher - 1950 - Journal of Symbolic Logic 15 (1):69-70.
  26.  1
    Dishkant Hermann. The First Order Predicate Calculus Based on the Logic of Quantum Mechanics. Reports on Mathematical Logic, No. 3 , Pp. 9–17.Georgacarakos G. N.. Orthomodularity and Relevance. Journal of Philosophical Logic, Vol. 8 , Pp. 415–432.Georgacarakos G. N.. Equationally Definable Implication Algebras for Orthomodular Lattices. Studia Logica, Vol. 39 , Pp. 5–18.Greechie R. J. And Gudder S. P.. Is a Quantum Logic a Logic? Helvetica Physica Acta, Vol. 44 , Pp. 238–240.Hardegree Gary M.. The Conditional in Abstract and Concrete Quantum Logic. The Logico-Algehraic Approach to Quantum Mechanics, Volume II, Contemporary Consolidation, Edited by Hooker C. A., The University of Western Ontario Series in Philosophy of Science, Vol. 5, D. Reidel Publishing Company, Dordrecht, Boston, and London, 1979, Pp. 49–108.Hardegree Gary M.. Material Implication in Orthomodular Lattices. Notre Dame Journal of Formal Logic, Vol. 22 , Pp. 163–182.Jauch J. M. And Piron C.. What is “Quantum-Logic”? Qu. [REVIEW]Alasdair Urquhart - 1983 - Journal of Symbolic Logic 48 (1):206-208.
  27. Review: Storrs McCall, A Simple Decision Procedure for One-Variable Implication/Negation Formulae in Intuitionist Logic. [REVIEW]Gene F. Rose - 1964 - Journal of Symbolic Logic 29 (4):212-212.
  28.  4
    The Transitivity of Implication in Tree Logic.N. L. Wilson - 1983 - Notre Dame Journal of Formal Logic 24 (1):106-114.
  29.  1
    Prior AN. The Theory of Implication. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 9 (1963), Pp. 1–6. Prior AN. The Theory of Implication: Two Corrections. Zeitschrift Für Mathematische Logik Und Grundlagen der Mathematik, Vol. 11 (1965), Pp. 381–382. Sobociński Bolesław. A Note on Prior's Systems in “The Theory of Deduction.” Notre Dame Journal of Formal Logic, Vol. 5 No. 2 (1964), Pp. 139–140. [REVIEW]Alan Ross Anderson - 1997 - Journal of Symbolic Logic 31 (4):665-666.
  30.  1
    Review: Dag Prawitz, Concerning Constructive Logic and the Concept of Implication[REVIEW]Dagfinn Follesdal - 1968 - Journal of Symbolic Logic 33 (4):605-605.
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  31.  1
    Implication in Equational Logic.H. G. Forder & J. A. Kalman - 1971 - Journal of Symbolic Logic 36 (1):162-162.
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  32.  1
    Review: H. G. Forder, J. A. Kalman, Implication in Equational Logic. [REVIEW]Ralph Seifert - 1971 - Journal of Symbolic Logic 36 (1):162-162.
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  33. Knox J. Jr., Material Implication and “If… Then.” International Logic Review—Rassegna Internazionale di Logica , Vol. 2 No. 3 , Pp. 90–92. [REVIEW]Alonzo Church - 1972 - Journal of Symbolic Logic 37 (1):185.
  34. Review: Z. P. Dienes, On an Implication Function in Many-Valued Systems of Logic. [REVIEW]Alonzo Church & Nicholas Rescher - 1950 - Journal of Symbolic Logic 15 (1):69-70.
  35. Thomas Ivo. The Rule of Excision in Positive Implication. Notre Dame Journal of Formal Logic, Vol. 3 , P. 64.Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):603.
  36. Schock Rolf. Some Definitions of Subjunctive Implication, of Counterfactual Implication, and of Related Concepts. Notre Dame Journal of Formal Logic, Vol. 2 , Pp. 206–221.Schock Rolf. A Note on Subjunctive and Counterfactual Implication. Notre Dame Journal of Formal Logic, Vol. 3 , Pp. 289–290. [REVIEW]Arnold Koslow - 1970 - Journal of Symbolic Logic 35 (2):319.
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  37. A Simplified Account of Validity and Implication for Quantificational Logic.Leblanc Hugues - 1970 - Journal of Symbolic Logic 35 (3):466-467.
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  38. Hacking Ian. What is Strict Implication? The Journal of Symbolic Logic, Vol. 28 No. 1 , Pp. 51–71.David Makinson - 1972 - Journal of Symbolic Logic 37 (2):417.
  39. A Simple Decision Procedure for One-Variable Implication/Negation Formulae in Intuitionist Logic.Mccall Storrs - 1964 - Journal of Symbolic Logic 29 (4):212-212.
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  40. Deontic Logic as Based on a System of Analytic Implication (Abstract).Carlos A. Oller - 1993 - Journal of Symbolic Logic 58 (4):1477-1478.
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  41. McCall Storrs. A Simple Decision Procedure for One-Variable Implication/Negation Formulae in Intuitionist Logic. Notre Dame Journal of Formal Logic, Vol. 3 , Pp. 120–122. [REVIEW]Gene F. Rose - 1964 - Journal of Symbolic Logic 29 (4):212-213.
  42. Review: Hugues Leblanc, A Simplified Account of Validity and Implication for Quantificational Logic. [REVIEW]A. Trew - 1970 - Journal of Symbolic Logic 35 (3):466-467.
  43. Ashworth E. J.. Propositional Logic in the Sixteenth and Early Seventeenth Centuries. Notre Dame Journal of Formal Logic, Vol. 9 No. 2 , Pp. 179–192.Ashworth E. J.. Petrus Fonseca and Material Implication. Notre Dame Journal of Formal Logic, Vol. 9 No. 3 , Pp. 227–228. [REVIEW]Martin M. Tweedale - 1971 - Journal of Symbolic Logic 36 (2):323-324.
  44. Implication and the Algebra of Logic.C. I. Lewis - 1912 - Mind 21 (84):522-531.
  45.  34
    The Logic of the "Educational Implication.Hobert W. Burns - 1962 - Educational Theory 12 (1):53-63.
  46.  34
    Implication, Modality and Intension in Symbolic Logic.Leo Abraham - 1933 - The Monist 43 (1):119-153.
  47.  13
    Inherent Logic Implication of Marx’s Thought of Human Happiness.汉华 王 - 2014 - Advances in Philosophy 3 (1):20-25.
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  48.  29
    On Truth, Implication, and Three-Valued Logic.Håkan Törnebohm - 1956 - Theoria 22 (3):185-198.
  49.  23
    On Implication (Tse) and Inference (Ku) in Chinese Grammar and Chinese Logic.Chung-Ying Cheng - 1975 - Journal of Chinese Philosophy 2 (3):225-244.
  50.  26
    Implication and Entailment in Navya-Nyāya Logic.V. K. Bharadwaja - 1987 - Journal of Indian Philosophy 15 (2):149-154.
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